To provide a solid understanding of vectors and tensor, it uses in every day life and wide applications in physical sciences.

INTENDED AND LEARNING OUTCOMES

Students will be able to articulate and describe:

1. The concepts of directional derivative, gradient and illustrating it geometrically with the aid of sketches.
2. Memorize theorem relating directional derivatives, the gradient and reproduce proofs.
3. to use directional derivatives and gradients in every day life.
4. To solve problems involving normal vectors to level surfaces.
5. Explain the concept of a vector integration a plane and in space.
6. All these activities will make the students more practical.
7. Physical intepreting will make them better understanding in the subject of mathematics.

COURSE CONTENTS:

1. Vectors analysis, Vectors Algebra,

2.Vector Differentiation and Gradient.

3. Divergence and Curl of a vector function

4. Gauss’s Theorem, Vector Integration,

5. Green’s Theorem in Plane, Curl and Stoke's theorem.

6. Curvilinear Coordinates: Orthogonal Coordinates in R3, Jacobian for Polar Coordinates.

7. Differential Vector Operator in Curvilinear Coordinates,

8. Circular Cylindrical Coordinates, Spherical Polar Coordinates.

9.Tensor Analysis: Covariant and Contravariant Tensors, Symmetric.

10. Antisymmetric Tensors, Direct Product and Contraction.

11. Quotient Rule, Pseudotensors, Dual Tensors, Metric Tensors, Christoffel Symbols.

12. Covariant Derivative, Geodesics, Parallel Transport,

13. Tensor Derivative Operators.

Recommended Books:

Sujected Books:

1. Mathematical Methods for Physicists by George Arfken and Hans J. Weber, (6th and onwards editions) Acad Press.

2. Differential Equations with boundary-value problems, by D. G. Zill, M. R. Cullen, PWS Publishing Co. (1997).

3. Cartesian Tensors by F. I. Zafar and M. S. Zafar. Majeed Book Depot, Lahore.

RESEARCH PROJECTS/ PRACTICAL/ LAB/ ASSIGNMENTS                             

Related topic assignments will be given to the students.

ASSESMENT CRITERIA

Sessional: 20(Presentation Assignmens 10, Attendence 05, Quiz 05)

Mid Term Exam: 30 Marks

Final Term Exam: 50 Marks

Key Dates and Time of Class Meeting: 

Wednesday: 8:00am-9:30am

Thursday: 8:00am-9:30am

Commicment of classes:              October 26, 2020

Mid Term Examination                  December 28, 2020

Final Term Examination                March 01-05, 2021

Declaration of Result                    March 12, 2021